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KCET2026MathematicsDifferential Equations

xf(x) ,dx + f(x) 2 = 0 , then f(x) is equal to

Options

  1. Ae^ -2x
  2. Be^ 2x
  3. Ce^ -x^2
  4. De^ x^2

Correct answer

C. e^ -x^2

Step-by-step solution

Differentiating the given equation with respect to x : x f(x) + 1 2 f'(x) = 0 f'(x) f(x) = -2x Integrating both sides with respect to x : f'(x) f(x) , dx = -2x , dx |f(x)| = -x^2 + C f(x) = A e^ -x^2 For A = 1 , f(x) = e^ -x^2 . Answer: e^ -x^2

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